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The weights of apples in a certain orchard follow a distribution with a mean of 150 grams and a standard deviation of 20 grams. If a random sample of 36 apples is taken, what is the standard error of the mean?

Sagot :

Answer:

The standard error of the mean (SEM) can be calculated using the formula:

\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} \]

where \(\sigma\) is the standard deviation of the population and \(n\) is the sample size.

Given:

- \(\sigma = 20\) grams

- \(n = 36\)

Substitute these values into the formula:

\[ \text{SEM} = \frac{20}{\sqrt{36}} = \frac{20}{6} = 3.33 \]

So, the standard error of the mean is 3.33 grams.